Escribir en un archivo de log la cadena XML que recibe un webservice

Dim httpStream As Stream = Context.Request.InputStream

Dim longitud As Integer = httpStream.Length
Dim buffer(longitud) As Byte

httpStream.Seek(0, 0)
httpStream.Read(buffer, 0, longitud)

Dim cad As String = System.Text.ASCIIEncoding.ASCII.GetString(buffer)

Dim path As String = Server.MapPath(".") + "\log2.txt"

Dim sw As StreamWriter = New StreamWriter(path, True)
sw.WriteLine("->" & Date.Now.ToString & cad)
sw.Close()

Evidentemente debes tener permiso de escritura sobre el directorio donde quieras guardar el log.